Modeling the fear effect in the predator-prey dynamics with an age structure in the predators

Wanxiao Xu; Ping Jiang; Hongying Shu; Shanshan Tong; Wanxiao Xu; Ping Jiang; Hongying Shu; Shanshan Tong

doi:10.3934/mbe.2023562

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12625-12648. doi: 10.3934/mbe.2023562

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Modeling the fear effect in the predator-prey dynamics with an age structure in the predators

1.
School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
2.
School of Management, Shanghai University of International Business and Economics, Shanghai 201620, China
3.
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, China

Academic Editor: Yang Kuang

Received: 05 April 2023 Revised: 15 May 2023 Accepted: 16 May 2023 Published: 26 May 2023

We incorporate the fear effect and the maturation period of predators into a diffusive predator-prey model. Local and global asymptotic stability for constant steady states as well as uniform persistence of the solution are obtained. Under some conditions, we also exclude the existence of spatially nonhomogeneous steady states and the steady state bifurcation bifurcating from the positive constant steady state. Hopf bifurcation analysis is carried out by using the maturation period of predators as a bifurcation parameter, and we show that global Hopf branches are bounded. Finally, we conduct numerical simulations to explore interesting spatial-temporal patterns.
- predator-prey dynamics,
- fear effect,
- reaction-diffusion system,
- maturation period,
- stability,
- hopf bifurcation
Citation: Wanxiao Xu, Ping Jiang, Hongying Shu, Shanshan Tong. Modeling the fear effect in the predator-prey dynamics with an age structure in the predators[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12625-12648. doi: 10.3934/mbe.2023562

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Abstract

We incorporate the fear effect and the maturation period of predators into a diffusive predator-prey model. Local and global asymptotic stability for constant steady states as well as uniform persistence of the solution are obtained. Under some conditions, we also exclude the existence of spatially nonhomogeneous steady states and the steady state bifurcation bifurcating from the positive constant steady state. Hopf bifurcation analysis is carried out by using the maturation period of predators as a bifurcation parameter, and we show that global Hopf branches are bounded. Finally, we conduct numerical simulations to explore interesting spatial-temporal patterns.

References

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